AUSTRALIAN domestic airline Ansett, which has promised cheap fares to attract Hong Kong tourists to Australia, has won its application to begin services to the territory. However, the airline, which is attempting to build an Asian network, has been granted fewer services than it sought and may appeal its case before the federal Government's International Air Services Commission. The commission, which determines rights to fly on routes granted under Australia's bilateral air agreements and capacities for each airline, granted Ansett the right to operate three Boeing 747 services a week between Sydney, Melbourne and Hong Kong fromApril next year and a further two 747s a week from April 1995. Ansett, owned by media group News Ltd and transport giant TNT, had sought daily flights. It also wanted to take over an extra seven B767-300 flights held by Qantas Airways as interim capacity until mid-1995 to allow it to fly to Hong Kong from Brisbane and Perth. The commission decided to leave that capacity with Qantas. Qantas operates 21 weekly flights each way between Australia and Hong Kong, including two 767-300 flights a week between Cairns, Brisbane and Hong Kong which were granted in October last year. Announcing the determination, commission chairman Jim Bain said it would increase airline capacity on the Hong Kong routes to 8,700 seats and 28 flights a week - a 40 per cent increase in the next two years. There would be significant public benefits from stronger competition, greater inbound tourism and consumer benefits, with visits by Hong Kong residents to Australia projected to rise from the current 82,000 a year to more than 100,000 by 2000, he said. Ansett's manager of aviation policy James Kimpton said: ''By and large we are pleased. We would have liked daily. One always wants daily in a market where one's competitors are daily.''